Yes, expenses incurred while on a medical missions trip would be deductible if the following conditions are met:
• Generally, you can claim a charitable contribution for travel expenses incurred while you are away from home performing services for a charitable organization. However, you cannot have any significant element of personal pleasure, recreation, or vacation in the travel.
• You can take a charitable contribution deduction for your travel expenses if you are on duty in a genuine and substantial sense throughout the trip. However, if you have only nominal duties, or if for significant parts of the trip you don't have any duties, you can't deduct your travel expenses.
• You can deduct your contributions only if you make them to a qualified organization. Most organizations other than churches and governments must apply to the IRS to become a qualified organization.
See
https://www.irs.gov/publications/p17/ch24.html#en_US_2015_publink100034100.
